This thesis investigates thresholds in an epidemic, heterogenenous model and how they are in uenced by the heterogeneity. First aepidemical models is introduced, where it could be optimal to treat at a maximal possible level or not to treat at all, depending on the particular parameters and initial state. Therefore an homogeneous epidemiological model is presented, whose heterogeneity is introduced with respect to the time the individual is already infected. Afterwards the optimal control problem is introduced for a restricted, constant control variable. The fourth section presents thresholds, rstly in a homogeneous version of the heterogeneous model. Based on these results, heterogeneity is introduced to the model and it is investigated how the thresholds are changing for dierent distribution functions. Finally a sensitivity analysis is conducted with respect to the infectivity of the disease.